Long story short, I think this is a an artifact of you messing around with saving into EmuMMC, and then transferring into SysNAND (which may or may not be successful).
There's also a chance your EmuMMC and SysNAND is presently "synced", so there's already some weirdness when handling saves.
(While this is thoroughly irrelevant to you, at some point I talk about 'syncing'.
More background: sometimes, an odd thing happens, where injecting a save into Emu causes the save to appear in Sys. So people expect it to be fine, to just inject into Emu. However when the Emu/sys 'desync', they'll complain to the forums that injecting stopped working, when in fact, you're not supposed to be able to directly inject into Sys from Emu; it working previously is unintended. You likely have to do some kind of transfer mentioned in the video [I did not watch it].)
In any case, this is not related to PKHeX, and until someone can reproduce it purely using SysNAND (no EmuMMC installed), I'm more or less convinced it is related to your setup.
I sadly won't be of much help since I don't use your setup.
edit: If your present EmuMMC is made recently, and it's made from a recent SysNAND, your profiles may very well be linked. Try injecting a save with Checkpoint in EmuMMC, and see if it shows up directly in SysNAND (like reboot your system and check).